Calculate the net force acting on a particle

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Mass transfer in a binary system
Calculate the net force acting on a particle
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Gravitational potential in the corotating frame
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Mass Transfer in Binary Stars
In a binary system, each star controls a finite
region of space, bounded by the Roche Lobes (or
Roche surfaces).
Lagrange points points of stability, where
matter can remain without being pulled towards
one of the stars.
Matter can flow over from one star to another
through the Inner Lagrange Point L1.
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How the matter from a star can be brought to L1
point?
Two mechanisms of mass transfer in a binary
system
Accretion through Roche lobe outflow
Accretion from stellar wind
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Accretion from a stellar wind
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Star overflows its Roche lobe
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Formation of an Accretion Disk The rotation of
the binary systems implies that gas flowing
through the L1 point will have relatively high
specific angular momentum - too much to directly
accrete onto a compact companion star.
                                                  
                                                  
                  
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Initial ring of gas spreads into the disk due to
diffusion.
To be able to accrete on the star, matter should
lose angular momentum as a result of viscous
friction Friction leads to heating of the disk
and intense radiation!!
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Accreting binary systems

• White dwarf binaries
• Neutron star binaries
• Black hole binaries

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Nova Explosions a mechanism
Hydrogen accreted through the accretion disk
accumulates on the surface of the WD

• Very hot, dense layer of non-fusing hydrogen on
  the WD surface

Nova Cygni 1975

• Explosive onset of H fusion

• Nova explosion

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Accreting neutron stars and black holes
Black holes and neutron stars can be part of a
binary system.
Matter gets pulled off from the companion star,
forming an accretion disk.
gt Strong X-ray source!
Infalling matter heats up to billions K.
Accretion is a very efficient process of energy
release.
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The Universe in X-ray and gamma-ray eyes
Giacconi Nobel prize 2002
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Accretion onto a neutron star
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X-ray pulsar an accreting neutron star
Compare with a radio pulsar
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Pulsars are slowing down with time. Millisecond
pulsars how can an old neutron star rotate at a
rate 1000/sec?
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Accretion onto black holes
There is no hard surface. Will there be any
radiation from the infalling matter??
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Cygnus X1 first black hole
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Measurement of binary system parameters gave M
7 Msun
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High-Mass X-ray binary accretion from a
wind Cygnus X1
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Low-Mass X-ray binary accretion through
Roche-lobe overflow
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Binary systems
If we can calculate the total mass and measure
the mass of a normal star independently, we can
find the mass of an unseen companion
a in AU P in years M1M2 in solar masses
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Low-mass X-ray binaries are best candidates
because the mass of a red dwarf is much less than
a black-hole mass
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Black-Hole vs. Neutron-Star Binaries
Black Holes Accreted matter disappears beyond
the event horizon without a trace.
Neutron Stars Accreted matter produces an X-ray
flash as it impacts on the neutron star surface.
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Soft X-ray transients (X-ray Novae)
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Black Hole X-Ray Binaries
Accretion disks around black holes
Strong X-ray sources
Rapidly, erratically variable (with flickering on
time scales of less than a second)
Sometimes Quasi-periodic oscillations (QPOs)
Sometimes Radio-emitting jets
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Radio Jet Signatures
The radio jets of the Galactic black-hole
candidate GRS 1915105
V 0.9 c
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Gamma-ray bursts
Discovered in 1968 by Vela spy satellites Occur
3 times a day at random positions in the sky
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Variability on a less than 1 ms timescale must
be a very small object
R lt ct 100 km
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Compton gamma-ray observatory discovered two
puzzles

• GRBs are distributed isotropically on the sky
• There is a deficiency of weak bursts are we
  looking over the edge of their distribution?

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GRB distribution
Gamma-ray sky
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Breakthrough in 1997 when BeppoSAX satellite was
able to detect the burst position at 1 arcmin
resolution and coordinate with optical telescopes
within 1 hour after the burst
An X-ray image of the gamma-ray burst GRB 970228,
obtained by the team of Italian and Dutch
scientists at 500 AM on Friday 28th February,
1997, using the BeppoSAX satellite.
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Discovery of the optical and radio counterparts
of GRBs
Spectral lines with redshift from 0.8 to almost 4!

• GRBs are at the edge of the observable universe
• They must be the most powerful explosions in the
  
• universe 1 solar mass is converted into
  gamma-rays
• in a second!

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Gamma-ray burst models
Hypernova??
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Known types of supernovae
Type II hydrogen lines collapse of a massive
star Type I no hydrogen lines
Fig. 10-18, p. 202
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Hard to imagine a supernova without ejection of a
star shell
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Colliding neutron stars
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Continuing cycle of stellar evolution
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Our Earth and our bodies are made of atoms that
were synthesized in previous generations of stars